7 is the best representation of the center of given data set.
The correct answer is an option (C).
What is center of data?
- "It is the middle of a distribution."
- "Mostly, The measures of the center of the data are the mean and the median."
What is mean?
"It is the average of the given numbers."
What is median?
"I is the middle value of a sorted list of numbers."
For given question,
We have been given a dot plot of the number of letters in each students first name.
From the given dot plot,
We have data as 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11
From above data,
the total number of students in the class are n = 30
We write 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11 as 3, (4 × 2), (5 × 4), (6 × 7), (7 × 7), (8 × 3), 9, (10 × 2), (11 × 3)
So, the mean of the above data would be,
[tex]\Rightarrow \bar{X}=\frac{3+ (4\times 2)+(5\times 4)+(6\times 7)+(7\times 7)+(8\times 3)+9+(10\times 2)+(11\times 3)}{30}\\\\\Rightarrow \bar{X}=\frac{208}{30}\\\\\Rightarrow \bar{X}=6.93\\\\\Rightarrow \bar{X}\approx 7[/tex]
From above data we can observe that there are two numbers in middle of the data 6 and 7.
So, the median would be,
[tex]\Rightarrow M=\frac{6+7}{2}\\\\\Rightarrow M=6.5\\\\\Rightarrow M\approx 7[/tex]
Therefore, 7 is the best representation of the center of given data set.
The correct answer is an option (C).
Learn more about the center of the data here:
https://brainly.com/question/17090777
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